Question: Simplify the following expression: $ r = -2 - \dfrac{5k + 3}{k + 5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k + 5}{k + 5}$ $ \dfrac{-2}{1} \times \dfrac{k + 5}{k + 5} = \dfrac{-2k - 10}{k + 5} $ Therefore $ r = \dfrac{-2k - 10}{k + 5} - \dfrac{5k + 3}{k + 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-2k - 10 - (5k + 3) }{k + 5} $ Distribute the negative sign: $r = \dfrac{-2k - 10 - 5k - 3}{k + 5}$ $r = \dfrac{-7k - 13}{k + 5}$